To calculate the average rate of change of the function \( f(x) = -x^2 + 12 \) over the interval \([2, 4]\), we can use the formula:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
where \( a = 2 \) and \( b = 4 \).
From the function table provided, we know:
- \( f(2) = 8 \)
- \( f(4) = -4 \)
Now we can substitute these values into the formula:
\[ \text{Average Rate of Change} = \frac{f(4) - f(2)}{4 - 2} = \frac{-4 - 8}{4 - 2} = \frac{-12}{2} = -6 \]
Thus, the average rate of change over the interval \([2, 4]\) is \(-6\).
The correct response is:
\(-6\)